Question

Find an equation of a plane containing the three points (4,0,4), (6,5,-5), and (6,6,-3) with the coefficient of X as 11. Which equation represents the plane?

a) 11x - 3y + 2z = 35
b) 11x + 3y - 2z = 35
c) 11x + 2y - 3z = 35
d) 11x - 2y + 3z = 35

Answer 1

To find the equation of a plane containing three points, use the formula Ax + By + Cz = D. Substitute the coordinates of the points to find A, B, C, and D. The correct equation is d) 11x - 2y + 3z = 35.

Step-by-step explanation:

To find an equation of a plane containing the three points (4,0,4), (6,5,-5), and (6,6,-3), we can use the formula Ax + By + Cz = D. First, we need to find the values of A, B, C, and D using the given points. We can do this by forming a system of three equations with the coordinates of the points and solving for A, B, C, and D. The resulting equation will be the equation of the plane. Using the three given points, the equation of the plane is 11x - 2y + 3z = 35. Therefore, the correct answer is d) 11x - 2y + 3z = 35.